Finite Group Databasebeta

← #11882318

Subgroups — #11882318

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596196C211yesmaximal, characteristic, complemented
2#10596051C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592726C211yesmaximal, characteristic, complemented
6#10592590C212yesmaximal, complemented
7#10592582C212yesmaximal, complemented
8#10592542C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592518C212yesmaximal, complemented
11#10592506C212yesmaximal, complemented
12#81131—34nomaximal
13C2×#3832—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64156—21no—
17#64156C2211yescharacteristic
18#64155C2211yescharacteristic
19C2×#3755C2212yes—
20C2×#3745C2212yes—
21C2×C8×C3⋊D3C2212yes—
22#64107—21no—
23#64104—21no—
24#64104C2211yescharacteristic
25#64104C2212yes—
26#64103—21no—
27#64102—21no—
28#64102C2212yes—
29#64099C2211yescharacteristic
30#64083C2211yescharacteristic
31C4×C4⋊(C3⋊D3)—21no—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33#64081—21no—
34C42×C3⋊D3C2211yescharacteristic
35C32×#107C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37C32×#103C2212yes—
38#63648C2212yes—
39#63641C2212yes—
40#63636C2212yes—
41#63636C2212yes—
42#63635C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5725—34no—
45#5580—34no—
46C3×#477D314yescomplemented
47#5084—34no—
48#5027—34no—
49#4891—38no—
50#4883—38no—
51#4843—34no—
52D3×C4⋊C8—34no—
53#4819—38no—
54#4807—38no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2311yescharacteristic
57#3832—44no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2311yescharacteristic
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2312yes—
74C32×C42—21no—
75C32×C42C2311yescharacteristic
76#3755—42no—
77#3752—21no—
78#3752—21no—
79#3752—21no—
80#3752—21no—
81#3752—21no—
82#3752—22no—
83#3752—22no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—21no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92#3745—42no—
93C8×C3⋊D3—42no—
94#3247—91noSylow
95C2×#239—64no—
96C3×C4⋊Q8C2×D314yes—
97C3×C4×Q8C2×D314yes—
98#947—34no—
99#947—64no—
100#946—34no—
101C2×#215—38no—
102C2×D24—38no—
103C2×D3×C8—38no—
104#898—64no—
105#895—34no—
106#895—38no—
107#895—64no—
108#894—64no—
109#893—38no—
110#893—64no—
111#890—34no—
112#874—34no—
113C4×D12—34no—
114C4×D12—64no—
115#872—64no—
116C42×D3—34no—
117C3×#107C2×D318yes—
118C3×C4⋊C8C2×D314yes—
119C3×#103C2×D318yes—
120#821—38no—
121Dic3⋊C8—38no—
122#809—38no—
123#809—38no—
124#808—38no—
125C4⋊(C3⋊C8)—34no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—21no—
130C32×Q8—21no—
131C32×Q8—42no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—21no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—42no—
147C4⋊(C3⋊D3)—42no—
148C4⋊(C3⋊D3)—44no—
149C4⋊(C3⋊D3)—42no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—21no—
153C4×C3⋊D3—21no—
154C4×C3⋊D3—44no—
155C4×C3⋊D3—42no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158#532—91no—
159#529—91no—
160#478—92no—
161#477C3⋊D311yescharacteristic, complemented
162#476—91no—
163#466—92no—
164#465—92no—
165#463—92no—
166#460—91no—
167#459—91no—
168C2×C4⋊C8—91no—
169C2×C3×Q8—24no—
170C2×C3×Q8C22×D314yes—
171#239—1216no—
172C2×D12—34no—
173C2×D12—38no—
174C2×D12—64no—
175C2×D12—68no—
176C2×D12—64no—
177C2×D12—64no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—34no—
181C2×C4×D3—68no—
182C2×C4×D3—64no—
183C2×C3×C8C22×D318yes—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D318yes—
187C3×C4⋊C4C22×D314yes—
188C3×C42—24no—
189C3×C42C22×D314yes—
190#215—128no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—64no—
198C4⋊Dic3—34no—
199C4⋊Dic3—64no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C2×C3⋊C8—38no—
206D24—128no—
207D3×C8—128no—
208C22×C32C22×D411yescharacteristic
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3—41no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—41no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3AGL(1,ℤ/8)12yes—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—42no—
221C32×C4—41no—
222C32×C4#13512yes—
223C32×C4H(5,𝔽2)11yescharacteristic
224C32×C42−1+411yescharacteristic
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C3⋊Dic3—41no—
229C2×#41—181no—
230C2×SD16—92no—
231C2×D8—92no—
232C22×C8—92no—
233C4⋊Q8C2×C3⋊D311yescharacteristic
234#127—91no—
235#126—181no—
236#125—91no—
237#124—91no—
238#124—181no—
239#123—181no—
240C22⋊Q8—91no—
241#121—91no—
242#121—92no—
243#121—181no—
244C4×Q8C2×C3⋊D311yescharacteristic
245C4×D4—92no—
246C4×D4—91no—
247C4×D4—181no—
248C4×D4—181no—
249#117—181no—
250C2×C42—91no—
251#107C2×C3⋊D312yes—
252#106—92no—
253C4⋊C8—92no—
254C4⋊C8—91no—
255C4⋊C8C2×C3⋊D311yescharacteristic
256#103C2×C3⋊D312yes—
257#102—92no—
258#102—92no—
259#102—92no—
260C22×D3—34no—
261C22×D3—64no—
262C22×D3—68no—
263C3×Q8—24no—
264C3×Q8—24no—
265C3×Q8—48no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—28no—
269C2×C3×C4D3×D414yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4C23×D314yes—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—64no—
276D12—64no—
277D12—68no—
278D12—64no—
279D12—68no—
280D12—128no—
281D12—128no—
282D12—1216no—
283D12—128no—
284C4×D3—68no—
285C4×D3—68no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—1216no—
289C4×D3—128no—
290C3×C8—28no—
291C3⋊C8—68no—
292C2×C32#53711yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
295C3⋊D3—22no—
296C3⋊D3—81no—
297C3⋊D3—82no—
298#41—364no—
299C2×Q8—21no—
300C2×Q8C22×C3⋊D311yescharacteristic
301C2×D4—91no—
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—182no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—182no—
311C22×C4—181no—
312SD16—362no—
313D8—362no—
314C2×C8—92no—
315C2×C8—362no—
316C2×C8C22×C3⋊D312yes—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4C22×C3⋊D311yescharacteristic
324C4⋊C4C22×C3⋊D312yes—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C42—21no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42C22×C3⋊D311yescharacteristic
337C22×C3C2×D3×D414yes—
338C2×D3—38no—
339C2×D3—64no—
340C2×D3—64no—
341C2×D3—124no—
342C2×D3—128no—
343C2×D3—128no—
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—128no—
347C3×C4—24no—
348C3×C4—48no—
349C3×C4—44no—
350C3×C4—44no—
351C3×C4#91918yes—
352C3×C4#100714yes—
353C3×C4#100914yes—
354Dic3—64no—
355Dic3—64no—
356Dic3—64no—
357Dic3—124no—
358C32#324711yescharacteristic, complemented, Sylow
359C23—91no—
360C23—181no—
361C23—182no—
362Q8—21no—
363Q8—21no—
364Q8—42no—
365D4—181no—
366D4—182no—
367D4—181no—
368D4—182no—
369D4—362no—
370D4—364no—
371D4—362no—
372D4—362no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—91no—
379C2×C4—182no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—182no—
383C2×C4—181no—
384C2×C4—364no—
385C2×C4—362no—
386C2×C4D4×C3⋊D311yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4C23×C3⋊D311yescharacteristic
389C8—22no—
390C8—182no—
391C2×C3#562914yes—
392C2×C3C2×#91914yes—
393C2×C3D3×AGL(1,ℤ/8)14yes—
394D3—68no—
395D3—244no—
396D3—248no—
397C22—92no—
398C22—181no—
399C22—181no—
400C22—361no—
401C22—362no—
402C22—361no—
403C22—362no—
404C22—362no—
405C22—361no—
406C22C2×D4×C3⋊D311yescharacteristic
407C4—21no—
408C4—41no—
409C4—42no—
410C4—41no—
411C4—181no—
412C4—181no—
413C4—181no—
414C4—361no—
415C4#6412812yes—
416C4#6436411yescharacteristic
417C4#6436611yescharacteristic
418C3#8113114yescomplemented
419C2—182no—
420C2—721no—
421C2—722no—
422C2#1059610011yescharacteristic
423C2C2×#6412811yescharacteristic
424C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#477C2
socleC22×C32C22×D4
hypercenter#477C3⋊D3
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596196C2semidirect
2. #10596051C2semidirect
3. C32×#477C2semidirect
4. #10592783C2semidirect
5. #10592726C2semidirect
6. #10592590C2semidirect
7. #10592582C2semidirect
8. #10592542C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
10. #10592518C2semidirect
11. #10592506C2semidirect
46. C3×#477D3semidirect
161. #477C3⋊D3semidirect
358. C32#3247semidirect
418. C3#81131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105961962
#105960512
C32×#4772
#105927832
#105927262
#105925902
#105925822
#105925422
C3⋊D3×C4⋊C82
#105925182
#105925062
#811313